Dodecahedral Adjoku

For the following puzzle, we return to the corners of the dodecahedon.  The goal is to fill in the cells with the numbers one through five so that the distance (or positive difference) is prime if, and only if the edge is colored in.  Each number can only be used four times, and no edge can end in cells of the same number.  The purple edges are intentionally thicker so that the puzzle can still be solved when printed in black and white.

High quality PDF for printing.

In case you're wondering why I chose the name Adjoku, note that the distance between two numbers is prime exactly when the two numbers fail to be adjacent modulo five.  Thus the rule set is identical to one based on adjacency.

Since there aren't nearly as many cells as a Sudoku this puzzle may appear simple, but it requires using all the given information wisely in order to arrive at a solution.